Tag
Proposes a hybrid least squares/gradient descent method for MIONets to accelerate training by using alternating least squares for the last layer parameters of multiple branch networks, leveraging Kronecker and Khatri-Rao products.
This paper presents MCO-PDE, a competitive optimization framework that discovers shared partial differential equations from multiple observational datasets by combining neural surrogates, soft-competitive weighting, and genetic algorithms for structure search. It demonstrates high accuracy in recovering canonical equations from limited data and handles complex geometries and real-world experiments.
This paper studies transfer specificity in implicit neural representations across SIREN, ReLU MLPs, and Fourier-feature MLPs, finding that transfer magnitude and specificity depend on architecture, with ReLU being more selective and SIREN reusing weights broadly. Results suggest architecture selection should consider explicit control conditions, not just transfer magnitude.
This paper establishes an exact correspondence between neural network training and Hamilton-Jacobi initial-value problems, unifying deep learning architectures through a deformation parameter.
The paper introduces beignet, a PINN architecture that replaces random Fourier features with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy and computational efficiency on PDE benchmarks.
This paper introduces breakeven complexity, a metric to determine when neural PDE solvers become cost-effective compared to traditional numerical solvers. The framework uses scaling laws to allocate training budgets and evaluates multiple neural solvers on diverse PDE benchmarks.
This paper proposes a spatially correlated curriculum learning framework for Physics-Informed Neural Networks (PINNs) that improves training stability and solution accuracy by leveraging spatial correlations among subregions, addressing issues like high-dimensional non-convex loss landscapes and imbalanced multi-objective constraints.
This paper extends Port-Hamiltonian Neural Networks (PHNNs) to partial differential equations (PDEs) for learning nonlinear string dynamics from data. The approach recovers both the Hamiltonian and dissipation, outperforming non-physics-informed baselines in accuracy and interpretability.